A sustainable urban park should have balanced green space (GS) supply and demand (SAD). A knowledge gap exists to reveal parameters that can indicate the relationship between the supply of GS services and the demand of public health needs. In this study, three primary indicators and 12 secondary indicators were selected to build a comprehensive evaluation system on SAD in the GSs of 14 parks along the “Luck Greenway” in Fuzhou. Parks were categorized and assessed for their ecological service functions, public health demands, and current public health needs. Remote evaluation and field survey were both used to collect data for quantifying functional supply and needs, respectively. It was found that factors, such as the fitness of sports service facilities, vegetation coverage, natural confluence, and mental health, impacted the comprehensive quality of supply services in urban parks. The unbalanced “multi-center” distribution of the coupled evaluation values revealed the mismatch in SAD. This study aimed to provide guidance on planning the health-promoting GS landscape by balancing SAD and maintaining ecological environment protection.